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Culture War Roundup for the week of January 15, 2024

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I think there are two important lenses here.

Via the probability-theory lens, we must distinguish between

  • the propensity for the coin to land on heads - unknown
  • the subjective (in the Bayesian sense) probability Yudkowsky assigns to the coin landing on heads on the next flip

Under a Bayesian epistemology, the former is reasoned about using a probability density function (PDF) by which (approximately) every number between 0 and 1 is assigned a subjective probability. Then, when we observe the flip we update using the likelihood function (either x for heads or 1-x for tails). What you're talking about is essentially how spread out Yudkowsky's current PDF is.

The other lens is markets-based, which I've touched on before. Briefly, for reason that are obvious for anyone in finance, there is a world of difference between

  • believing a stock is worth X
  • offering to buy the stock for X+0.01 from anyone and sell it for X-0.01 to anyone

In real life, the bid-ask spread that market makers offer depend on a great number of factors including how informed everyone else in the market is relative to themselves. On this lens, credible intervals (or whatever phrase you want to use) are not things individuals have in isolation, they are things individuals have within a social space: if you're with a bunch of first-graders, you might have a very tight bid-ask spread when betting on whether a room-temperature superconductor was just discovered; if you're with a bunch of chemist PhDs, you're going to adopt an extremely wide spread (e.g. "somewhere between 5% and 95%").